NMR Spectroscopy

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Example:
How many protein molecules are there in the solution sample (volume, 100 ml) at the concentration of 0.1 mM?
About samples of biomolecules

Slide 4

1 mm particles
Brownian motion

Slide 5

1785: Jan Ingenhousz observed irregular motion of coal dust particles in alcohol.
1827: Robert Brown watched pollen particles performing irregular motion in water using a microscope. He repeated his experiments with dust to rule out that the particles were alive.
1905: Einstein provided the first physical theory to explain Brownian motion.
1908: Jean Perrin did experiments to verify Einstein’s predictions. The measurements allowed Perrin to give the first estimate of the dimensions of water molecules. Jean Perrin won the Nobel Prize of Physics in 1926 for this work.
History of Brownian motion

Slide 6

Each step in the x and y directions are random, but otherwise equal, such that qx2=qy2
Random walk

Fick’s law of diffusion
Adolf Fick (1855):
J= flux of particles (number of particles per area and time incident on a cross-section) [m-2s-1]
D= diffusion coefficient [m2s-1]
C=concentration of particles [m-3]
(sometimes n is used instead of C to represent concentration )
J
A

Slide 9

Random walk is due to thermal fluctuations!
v
R(t)

Slide 10

Diffusion coefficients in different materials

Slide 11

Radiation
X-ray
n
e-
RF

Slide 12

Photons and Electromagnetic Waves
Light has a dual nature. It exhibits both wave and particle characteristics
Applies to all electromagnetic radiation

Wave Properties of Particles
In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties

Slide 16

de Broglie Wavelength and Frequency
The de Broglie wavelength of a particle is
The frequency of matter waves is

Slide 17

Dual Nature of Matter
The de Broglie equations show the dual nature of matter
Matter concepts
Energy and momentum
Wave concepts
Wavelength and frequency

Slide 18

X-Rays
Electromagnetic radiation with short wavelengths
Wavelengths less than for ultraviolet
Wavelengths are typically about 0.1 nm
X-rays have the ability to penetrate most materials with relative ease
Discovered and named by Röntgen in 1895

Slide 19

Production of X-rays
X-rays are produced when high-speed electrons are suddenly slowed down

Slide 20

Wavelengths Produced

Slide 21

European synchrotron
Grenoble, France
Production of X-rays in synchrotron

Slide 23

European synchrotron
Electron energy: 6 Gev

Slide 24

European synchrotron
Bending magnets
Undulators

Slide 25

A typical beamline

Slide 26

The three largest and most powerful synchrotrons in the world
APS, USA
ESRF, Europe-France
Spring-8, Japan

Schematic for X-ray Diffraction
The diffracted radiation is very intense in certain directions
These directions correspond to constructive interference from waves reflected from the layers of the crystal

Bragg’s Law
The beam reflected from the lower surface travels farther than the one reflected from the upper surface
Bragg’s Law gives the conditions for constructive interference
2 d sinθ = mλ; m = 1, 2, 3…

The Electron Microscope
The electron microscope depends on the wave characteristics of electrons
Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object
The electrons can be accelerated to high energies and have small wavelengths